The present invention relates to the construction of profiles of conjugate gears. In particular, the present invention relates to the construction of profiles of conjugate gears having a relative curvature which is a function of gear ratio, face-width factor, center distance and limiting stresses.
In U.S. Pat. No. 6,101,892, incorporated herein by reference, three methods were described for specifying the curvatures of conjugate tooth profiles. If s, φ are the polar coordinates of points on the path of contact, and ρ1, ρ2 are the profile radii of curvature at the corresponding points on the tooth profiles, these methods can be stated as follows:1/ρ1+1/ρ2=Constant  (1)(1/ρ1+1/ρ2)/cos φ=Constant  (2)f(s,φ,ρ1,ρ2)=Constant  (3)
The first method can be described as constant relative curvature. The second method is suitable for spur gears, and is intended to provide constant contact stress. In the third method, f can be any function, specified by the designer of the tooth profiles. For conventional gears, such as involute gears, if the load intensity is known, i.e. the tooth force per unit length of the contact curve, then the tooth stresses can be found by conventional, well known methods.
However, finding the load intensity for a given torque is more difficult for Convoloid gears than for involute. In an involute gear pair, the contact curves are straight lines, and at every point of a contact line the normal to the tooth surface points in the same direction, so that for a given torque the load intensity is inversely proportional to the total length of the contact lines. The maximum load intensity is found when the total length of the contact lines is a minimum, and this occurs when one contact line passes through a corner of the contact region.
In a Convoloid gear pair, by contrast, the contact curves are not exactly straight, the normals do not point in exactly the same direction, and the contact curves are broken where they cross the transition zone. Hence, the load intensity is not inversely proportional to the total length of the contact curves, and the position of the contact curves for maximum load intensity is not known.
Accordingly, it is desirable to design Convoloid gear pairs having a relative curvature for which the maximum stresses approach but do not exceed the limiting stresses.